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Math Help - How to prove this (about determinants)

  1. #1
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    How to prove this (about determinants)

    honestly ive searched through the stickied posts (compilation of proofs) and some other threads, but i think i was just too blind to see it if this was already posted,

    anyway, i was told that:
    if a row/column of a matrix is a SCALAR MULTIPLE of another (in the same matrix)
    then its det is 0,

    hmm, i really tried this with some examples and its true,
    can anyone prove this? i dont wanna present my answer without any proofs
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  2. #2
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    Think of rules about interchanging, adding, subtracting rows/columns in a determinant. Then think of easy ways to calculate a determinant.
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  3. #3
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    Quote Originally Posted by experiment00 View Post
    honestly ive searched through the stickied posts (compilation of proofs) and some other threads, but i think i was just too blind to see it if this was already posted,

    anyway, i was told that:
    if a row/column of a matrix is a SCALAR MULTIPLE of another (in the same matrix)
    then its det is 0,

    hmm, i really tried this with some examples and its true,
    can anyone prove this? i dont wanna present my answer without any proofs
    By performing a simple elementary row operation you can get a matrix with a row/column whose entries are all zero. This matrix will have the same determinant as the original. Therefore ....
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  4. #4
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    i see!
    so if make these rows/columns (the other one being a multiple of the other) equal by extracting the "scale" (lol dunno the term) XD
    then negate one of these equal rows/columns, add both, viola!

    thanks a lot sirs!
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